To the best of my recollection, the first way is simply to name the thing wanted. "Milk! Milk!" "More! More!" is learned pretty quickly. "Gimme" and "Wan' dat" and "Wannit," too. At some point, maybe age 3? 4?, there is often a dialog that goes something like this: Child: "More cookies. Gimme cookies." Parent: "You have to say the 'magic word.'" Child: "Please!" Parent: "'May I have more cookies, please?'" Child: "Gimme more cookies.... pullllleeeez!" Parent: "Yes, you may have ONE more." (passes the cookies) Child (happily) "I gots cookie!"

The consonants 'm' and 'g' are among the first that babies master, so most infants can manage "Gimme..." fairly early on.

One of our "family stories" is about a time when my little brother was just learning to talk. The family had gone out for ice cream in a restaurant. After he'd finished his, he suddenly surprised everyone by saying, loudly, to the waitress: "Yaydee! Yaydee! Mo' ice cweam!" ("Lady! Lady! More ice cream!")

They usually just say the noun. "Juice." "Milk." "Teddy." This is followed by the caregiver saying some version of "say 'please'" in an attempt to teach the child to be polite. The child then follows with "Juice, please." After getting the item in question, the caregiver will then try to get the child to say "thank you," as complete sentences are far less important than manners.

Sometimes they just learn the nouns (or something that sounds like the noun) and say that. For example 'Drink'.